Problem: Rewrite as a simplified fraction. ${0.4\overline{59} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 459.5959...\\ 10x &= 4.5959...\end{align*}}$ Subtracting the two equations, we have: ${990x = 455}$ ${x = \dfrac{455}{990}} $ ${x = \dfrac{91}{198}} $